I've added my Google, Twitter, and Windows Live accounts without any issues.
However, when I try to add a Facebook account, instead of opening in the system dialogue for online accounts, it opens up a new Window in Chromium which seems a bit odd in the first place. Then, once I authorize Ubuntu to post on my behalf etc., I finish the authorization and Facebook redirects me to a page with just the word "Success" written on it.
Ubuntu still does not show that it is integrated with Facebook, but in my Facebook app settings, I can see clearly that it is authorized.
I should also note that I tried this when Firefox was set as default browser and it did the same thing, so it's not a Chromium issue.